Finite Group Databasebeta

← #14646789

Subgroups — #14646789

Order 2816.

404 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077328C211yesmaximal, characteristic
2#13067371C212yesmaximal, complemented
3#13067351C211yesmaximal, characteristic
4C11⋊#1309C212yesmaximal, complemented
5C11×#1560C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C2×#67001C412yes—
8C11×#423C2212yes—
9#10622847C412yes—
10#10622625—22no—
11D4×C11⋊C8—22no—
12#10622537C2212yes—
13#10622537C2211yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15C11×#333—21no—
16C11×#331—21no—
17#10622184—21no—
18#10622182—21no—
19#10622118—22no—
20#10622118—22no—
21C2×C11×#41C2×C412yes—
22C2×C11×M16—22no—
23C11×C4⋊Q8D411yescharacteristic
24C11×#127D411yescharacteristic
25C11×#124Q812yes—
26C11×#121—22no—
27C4×D4×C11—22no—
28C2×C42×C11C2311yescharacteristic
29#67001—44no—
30C2×#4318—22no—
31C2×#4318—22no—
32C2×#4318C2×C412yes—
33C22×C11⋊C8—22no—
34C22×C11⋊C8C2×C411yescharacteristic
35C22×C11⋊C8C2×C411yescharacteristic
36C11×C4⋊C8—22no—
37C11×C4⋊C8—22no—
38C22⋊(C11⋊C8)—24no—
39C4⋊(C11⋊C8)—22no—
40C4⋊(C11⋊C8)—22no—
41C4⋊(C11⋊C8)—22no—
42C4×C11⋊C8D412yes—
43C4×C11⋊C8D412yes—
44#8636—111nomaximal, Sylow
45C11×#41—42no—
46C11×#41—42no—
47C2×Q8×C11C4⋊C412yes—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11C4⋊C412yes—
51C22×C4×C11—22no—
52C22×C4×C11C22×C411yescharacteristic
53C22×C4×C11#4112yes—
54C11×M16—82no—
55C2×C8×C11—42no—
56C11×C4⋊C4—22no—
57C11×C22⋊C4—24no—
58C42×C11C2×D412yes—
59C42×C11C2×D411yescharacteristic
60C42×C11C2×Q811yescharacteristic
61#4318—42no—
62#4318—44no—
63#4318—82no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8—22no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8—44no—
68C2×C11⋊C8—42no—
69C2×C11⋊C8C22⋊C412yes—
70C2×C11⋊C8C22⋊C411yescharacteristic
71C2×C11⋊C8C22⋊C411yescharacteristic
72#2931—111no—
73#1566—112no—
74#1560—111no—
75#1560D1111yescharacteristic
76#1309—112no—
77C23×C11—22no—
78C23×C11#11711yescharacteristic
79Q8×C11—42no—
80D4×C11—42no—
81D4×C11—44no—
82D4×C11—42no—
83D4×C11—42no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11C2×C22⋊C411yescharacteristic
92C2×C4×C11C2×C4⋊C411yescharacteristic
93C2×C4×C11#12112yes—
94C2×C4×C11C22⋊Q812yes—
95C8×C11—82no—
96C11⋊C8—21no—
97C11⋊C8—22no—
98C11⋊C8—42no—
99C11⋊C8—82no—
100C11⋊C8#10012yes—
101C2×#131—112no—
102#532C2×D1111yescharacteristic
103#436—222no—
104C8×D4—222no—
105#423—111no—
106#423—112no—
107#423C2×D1112yes—
108#408—112no—
109C2×C4×C8—111no—
110#334—222no—
111#334—222no—
112#333—21no—
113#333—221no—
114#331—21no—
115#331—221no—
116C22×C11—21no—
117C22×C11—22no—
118C22×C11—42no—
119C22×C11—44no—
120C22×C11#38011yescharacteristic
121C4×C11—21no—
122C4×C11—22no—
123C4×C11—42no—
124C4×C11C2×#10011yescharacteristic
125C4×C11#41311yescharacteristic
126C4×C11#47112yes—
127C4×C11#47112yes—
128C2×#41C4×D1112yes—
129#131—444no—
130C2×M16—22no—
131C2×M16—112no—
132C2×M16—222no—
133C2×M16—222no—
134C22×C8—111no—
135C22×C8—111no—
136C22×C8—222no—
137C4⋊Q8C22⋊D1111yescharacteristic
138#127C22⋊D1111yescharacteristic
139#124Dic2212yes—
140#121—22no—
141C4×D4—22no—
142C2×C42C22×D1111yescharacteristic
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8—222no—
146C4⋊C8—222no—
147C4⋊C8—222no—
148C22⋊C8—224no—
149C4×C8—112no—
150C4×C8—112no—
151C2×C11—41no—
152C2×C11—82no—
153C2×C11#180011yescharacteristic
154C2×C11#181512yes—
155#41—42no—
156#41—42no—
157C2×Q8Dic11⋊C412yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4Dic11⋊C412yes—
161C22×C4—22no—
162C22×C4C2×C4×D1111yescharacteristic
163C22×C4#434112yes—
164M16—82no—
165M16—444no—
166M16—442no—
167M16—882no—
168C2×C8—42no—
169C2×C8—111no—
170C2×C8—112no—
171C2×C8—111no—
172C2×C8—222no—
173C2×C8—222no—
174C2×C8—444no—
175C2×C8—441no—
176C2×C8—442no—
177C4⋊C4—22no—
178C22⋊C4—24no—
179C42C2×Dic2211yescharacteristic
180C42D4×D1112yes—
181C42C2×C22⋊D1111yescharacteristic
182C11#863611yescharacteristic, complemented, Sylow
183C23—22no—
184C23#6693011yescharacteristic
185Q8—42no—
186D4—42no—
187D4—44no—
188D4—42no—
189D4—42no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4#6693112yes—
198C2×C4C22⋊C4×D1111yescharacteristic
199C2×C4C2×Dic11⋊C411yescharacteristic
200C2×C4#6699212yes—
201C8—82no—
202C8—112no—
203C8—221no—
204C8—222no—
205C8—442no—
206C8—882no—
207C22—21no—
208C22—22no—
209C22—42no—
210C22—44no—
211C22#1062255511yescharacteristic
212C4—21no—
213C4—22no—
214C4—42no—
215C4D11×#10011yescharacteristic
216C4#1062235811yescharacteristic
217C4#1062281312yes—
218C4#1062281612yes—
219C2—41no—
220C2—82no—
221C2#1306860611yescharacteristic
222C2#1306867312yes—
subgroupG/H
centerC22#10622555
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1560C2
socleC22×C11#380
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1560D11
hypocenterC11#8636
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1560

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13067371C2semidirect
4. C11⋊#1309C2semidirect
182. C11#8636semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130773282
#130673712
#130673512
C11⋊#13092
C11×#15602
#863611